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CRANES I Mechanical Engineering Department Carlos III University CRANES TRANSPORTATION CRANES I INTRODUCTION • Crane: device used to lift or lower materials in the vertical direction and to move them horizontally while being hanged. • UNE 58-104-87. Part 1. Types of transport elevators: – – – – According to design. According to movement possibilities. According to device control. According to orientation possibilities. 1 CRANES I INTRODUCTION • The dynamic structural calculation allows to determine the stress of the elevator during its operation. • Phases: 1. 2. 3. Find the external forces and their combination, that act on the structure. Displacement, stress and reaction calculation of each of the components applying the adequate calculation process. Verification of the obtained values of elasticity, resistance and stability. Nowadays: Finite element programs are used CRANES I INTRODUCTION • Loads to be considered: – Principal loads acting on the structure for the motionless elevator. The worst loads are: • • – Loads due to vertical movements: • • – Normal operation load: service load + accessories Self weight: crane components weight (set aside operation load) Accelerations or decelerations Vertical impacts due to the rollers Loads due to horizontal movements: • • • • Accelerations or decelerations Centrifugal force Lateral effects due to rolling Impact effects – Loads due to changes in climate: – Various loads: • • Wind, snow and temperature effects Dimensioning of rails and aisles 2 CRANES I STRUCTURAL CALCULATION: CASE I • CASE I: Without wind: – The next loads are considered: static due to self weight SG, forces due to service load SL multiplied by the dynamic coefficient ψ and the two most unfavourable horizontal effects SH, set aside impact effects, multiplied by an increase factor γc: γ c ( SG +ψSL +SH ) – Increasing factor γc [UNE 58132-2] : Depends on the elevator classification group Elevator group A1 A2 A3 A4 A5 A6 A7 A8 γc 1,00 1,02 1,05 1,08 1,11 1,14 1,17 1,20 CRANES I STRUCTURAL CALCULATION: CASE I γ c ( SG +ψSL +SH ) • Dynamic coefficient ψ: takes into account – – – The service load lifting. The accelerations and decelerations in the lifting process. The vertical impacts due to the rolling in the track. Ψ=1+ξVL VL is the lift speed in m/s ξ is an experimental coefficient obtained by carrying out several tests in different elevators 3 CRANES I STRUCTURAL CALCULATION: CASE I Bridge and gantry crane Jib crane CRANES I STRUCTURAL CALCULATION: TOWER CRANE G: crane weight Jib pendants Jib pendants Cat head Jib Counterweight jib Pi=Q+Pc (load+trolley) Gc: counterweight weight Mast It is important to know the maximum load depending on the position: its values are usually specified in points A and B 4 CRANES I STRUCTURAL CALCULATION: TOWER CRANE Above structure The jib pendants are subject to traction, while the cat head is subjected to compression, flexure and shear Traction forces in the jib ties T1 = PB sen ( β ) T1 = Gc T2 = sen ( α ) ψ ⋅ PB sen ( β ) Gc T2 = sen ( α ) σ1 = σ2 = T1 A1 T2 A2 Forces in the cat head are: V=T1 ⋅ sen ( β ) +T2 ⋅ sen ( α ) H=T1 ⋅ cos ( β ) -T2 ⋅ cos ( α ) M=H ⋅ h Von Misses V σc = Ap σf = τ= M Wpf H⋅m b ⋅ Iz σ T = σ 2 +3τ 2 σ T = (σ f + σ c ) 2 +3τ 2 m: first moment of the principal area CRANES I STRUCTURAL CALCULATION: TOWER CRANE Above structure The jib is subjected to flexure and shear forces: Von Misses M pl,f =PA ⋅ L3 M pl,f =ψ ⋅ PA ⋅ L3 Vpl,c =PA Vpl,c =ψ ⋅ PA ψ ⋅ PA ⋅ L3 σf = Wpf ψ ⋅ PA ⋅ m τ= b ⋅ Iz σ T = σ f2 +3τ 2 5 CRANES I STRUCTURAL CALCULATION: TOWER CRANE Mast M f =PB ⋅ L1 − G c ⋅ L 2 + G ⋅ e Vc =PB + G c + G The mast is subjected to flexure and compression forces Jib tie Jib tie Cat head Jib M f =ψ ⋅ PB ⋅ L1 − G c ⋅ L 2 + G ⋅ e Vc =ψ ⋅ PB + G c + G Counterweight jib Mf Vc L2 e L L1=L+e σf = ψ ⋅ PB ⋅ L1 − G c ⋅ L 2 + G ⋅ e Wmf σc = ψ ⋅ PB + G c + G Am Tower σ T =σ f + σ C CRANES I STRUCTURAL CALCULATION: CASE I γ c ( SG +ψSL +SH ) • Loads due to horizontal movements: – – – – Accelerations and decelerations due to translations movements of the crane Acceleration or decelerations due to movements of the load Centrifugal force Lateral effects due to rolling (loads due to obliquity) 6 CRANES I STRUCTURAL CALCULATION: CASE I γ c ( SG +ψSL +SH ) • Accelerations or decelerations of movements : – Accelerations/decelerations due to translation movements of the crane H= – a ⋅V g The acceleration/deceleration value depends on: • • • The desired speed Time to accelerate/decelerate Usage of the elevator CRANES I STRUCTURAL CALCULATION: CASE I Desired speed [m/s] (a) Low and medium speed with large travelling Time to accelerate [s] Acceleration [m/s2] (b) Medium and high speeds (usual applications) (c) High speed with great accelerations Time to accelerate [s] Acceleration [m/s2] Time to accelerate [s] Acceleration [m/s2] 4,00 8,00 0,50 6,00 0,67 3,15 7,10 0,44 5,40 0,58 2,50 6,30 0,39 4,80 0,52 2,00 9,10 0,22 5,60 0,35 4,20 0,47 1,60 8,30 0,19 5,00 0,32 3,70 0,43 1,00 6,60 0,15 4,00 0,25 3,00 0,33 0,63 5,20 0,12 3,20 0,19 2,50 0,16 0,40 4,10 0,098 0,25 3,20 0,078 0,16 2,50 0,064 7 CRANES I STRUCTURAL CALCULATION: CASE I γ c ( SG +ψSL +SH ) • Accelerations or decelerations of the load movement: – Inertia force of the load (with weight W): F= – Wa =ma g Rotational movement: T: Inertia moment J: Inertia polar moment = α: Angular acceleration T=Jα ∑m d i 2 i CRANES I STRUCTURAL CALCULATION: CASE I Inertia forces due to rotation: F=m e ⋅ a Equivalent mass me =∑ Tangencial acceleration 2 i i 2 md D F=α ⋅ ∑ a=α ⋅ D mi d i2 D 8 CRANES I STRUCTURAL CALCULATION: CASE I γ c ( SG +ψSL +SH ) • Loads due to obliquity: – – Tangential forces between the wheels and the rail track. Guide forces. • A simple translation mechanical model is needed: – – n pairs of wheels in line. p coupled pairs. Coupled (C) Individual (I) Fixed/Fixed (F/F) Fixed/Mobile (F/M) CRANES I STRUCTURAL CALCULATION: CASE I γ c ( SG +ψSL +SH ) • Loads due to centrifugal forces: – Effects of the cable inclination Fc = WR πn g 30 2 W: Load R: Radius n: Rotating speed g: gravity acceleration 9 CRANES I STRUCTURAL CALCULATION: CASE II • CASE II: Normal operation with service limit wind – To the loads considered in CASE I it is added the effect of service limit wind Sw and, if needed, the load due to variation in temperature: γ c ( SG +ψSL +SH ) + Sw – Overloading due to snow is not considered. CRANES I STRUCTURAL CALCULATION: CASE II γ c ( SG +ψSL +SH ) + Sw • Wind effect F=A ⋅ p ⋅ Cf •A is the net surface, in m2, of the considered element, that is, the solid surface projection over a perpendicular plane in the wind direction. •Cf is a shape factor, in the wind direction, for the considered element. •p is the wind pressure, in kN/m2, and it is calculated by means of the following equation: -3 2 p = 0, 613 ⋅10 ⋅ vs [kPa] where vs is the calculated wind speed in m/s 10 CRANES I STRUCTURAL CALCULATION: CASE II Cf: Shape factor [UNE 58-113-85] Type Simple elements Simple lattice work Machine room, etc Aerodynamic drag coefficient l/b or l/D Description 5 10 20 30 40 50 Metal section in L, in U and flat plates 1,3 1,35 1,6 1,65 1,7 1,9 Circular metal sections in which Dvs < 6 m2/s in which Dvs ≥ 6 m2/s 0,75 0,60 0,80 0,65 0,90 0,70 0,95 0,70 1,0 0,75 1,1 0,8 1,55 1,40 1,0 0,8 1,75 1,55 1,2 0,9 1,95 1,75 1,3 0,9 2,1 1,85 1,35 1,0 2,2 1,9 1,4 1,0 Square metal sections of more than 350 mm side and rectangular of more than 250 mm x 450 mm b/d ≥2 1 0,5 0,25 Flat side metal section 1,7 Circular metal sections in which Dvs < 6 m2/s in which Dvs ≥ 6 m2/s 1,2 0,8 Square structures filled (air cannot flow beneath the structure) 1,1 CRANES I STRUCTURAL CALCULATION: CASE II Wind Aerodynamic coefficient= Section proportion= Element length 1 1 = or Section height facing wind b D Section height facing wind b = Section width parallel to wind d 11 CRANES I STRUCTURAL CALCULATION: CASE II Speeds and pressures of service wind [UNE 58-113-85] Type of crane Wind speed m/s Wind pressure kPa/m2 Cranes which can be protected against wind and designed exclusively for light wind (for example, low height cranes with an easily folding jib to the ground) 14 0,125 Every normal crane installed in exteriors 20 0,25 28,5 0,50 Dock cranes that should continue operation in case of strong wind p = 0, 613 ⋅10-3 ⋅ vs2 [kPa] CRANES I STRUCTURAL CALCULATION: CASE II γ c ( SG +ψSL +SH ) + Sw • Snow overloading: – It is not considered • Temperature effect: – – Only when the elements cannot freely expand Temperature limit -20 ºC + 45 ºC 12 CRANES I STRUCTURAL CALCULATION: CASE III • CASE III: Elevator subjected to exceptional loads a) Elevator out of service subjected to maximum wind. b) Elevator in service subject to impact. c) Elevator subjected to static and dynamic tests. CRANES I STABILITY Wm d m > Wb d b + W d 13 CRANES I STABILITY Wm Rotation axis Wm d m + Wf ( d o − d f ) > Wb d b + Wr d CRANES I COUNTERWEIGHT CALCULATION It is usually calculated so that it counteracts the half of the material moment and the jib moment Moment: G c ⋅ d=G ⋅ e+(Pc + Q )⋅L 2 M f =(Pc + Qi ) ⋅ L+G ⋅ e-G c ⋅ d Q Q M f =(Pc + Qi ) ⋅ L+G ⋅ e- G ⋅ e+(Pc + ) ⋅ L = Qi − ⋅ L 2 2 P=Qi+Pc (Load+hoist) Most unfavourable situations: Without load: Qi=0 Q M f =- ⋅ L 2 With load: Qi=Q Mf = Q ⋅L 2 With this type of counterweight the mast, with and without load, has a uniform solicitation in a favourable way 14 CRANES I CLASSIFICATION Crane and elevators classification allows to establish the design of the structure and of the mechanisms It is used by manufacturers and clients so that a specific elevator operates within certain required service conditions. Elevator classification Used by the client and the manufacturer to achieve a fixed elevators service conditions Mechanism classification It gives the manufacturer information of how to design and verify the elevator so that it has the desired service life for the operation service conditions CRANES I CLASSIFICATION OF THE EQUIPMENT CLASSIFICATION OF THE EQUIPMENT (standard 58-112-91/1) Number of cycles of a manoeuvre Load spectrum coefficient A manoeuvre cycle begins when the load is prepared to be lifted and finishes when the elevator is prepared to lift the next load • The total number of manoeuvre cycles is the sum of all of the cycles carried out during the elevator life. • The user expects that the elevator’s manoeuvre number of cycles is achieved during its life. • The total number of manoeuvre cycles has a relationship with the usage factor: – The manoeuvre spectrum has been conveniently divided in 10 usage classes. 15 CRANES I CLASSIFICATION OF THE EQUIPMENT: TOTAL NUMBER OF CYCLES CRANES I CLASSIFICATION OF THE EQUIPMENT CLASSIFICACIÓN OF THE EQUIPMENT (standard 58-112-91/1) Number of cycles of a manoeuvre Load spectrum coefficient The load condition is the number of times a load is lifted, which is suitable to the elevator capacity • Depending on the available information of the number and weight of the loads to be lifted during the elevator life: – – Lack of indications: manufacturer and client have to achieve an agreement. If the information is available: the load spectrum coefficient of the elevator can be calculated. 16 CRANES I CLASSIFICATION OF THE EQUIPMENT : LOAD LEVEL C P 3 Kp = ∑ i i CT Pmax Ci is the mean number of cycles of manoeuvre for each different load level. CT is the total of the individual cycles for every load level. Pi are the values of the individual loads characteristic of the equipment service operation. Pmax is the maximum load that the equipment is authorized to lift (safe working load). CRANES I CLASSIFICATION OF THE EQUIPMENT : LOAD LEVEL 17 CRANES I CLASSIFICATION OF THE COMPLETE EQUIPMENT CRANES I CLASSIFICATION OF THE COMPLETE EQUIPMENT 18 CRANES I CLASSIFICATION OF THE MECHANISM CLASSIFICACIÓN OF THE MECHANISMS (standard 58-112-91/1) Usage of work equipment Mechanism load level It is calculated for the planned service duration in hours • Maximum service duration can be computed by means of the mean daily service, in hours, of the number of working days per year and the number of the planned years of service. • A mechanism is considered to be on service when it is on movement. CRANES I CLASSIFICATION OF THE MECHANISM: USAGE 19 CRANES I CLASSIFICATION OF THE MECHANISM CLASSIFICACIÓN OF THE MECHANISMS (standard 58-112-91/1) Use of work equipment Loads applied to the mechanism The load level is a feature that shows how much a mechanism is subjected to a maximum load, or only to low loads. t k m =∑ i Tt 3 Pi Pmax ti is the mean service duration of the mechanism when subjected to individual loads. Tt iis the sum of the individual durations in all load level Pi is the individual load level of the mechanism Pmax is the maximum load applied to the mechanism CRANES I CLASSIFICATION OF THE MECHANISM: APPLIED LOAD 20 CRANES I CLASSIFICATION OF THE MECHANISM CRANES I CLASSIFICATION OF THE MECHANISM 21 CRANES I CLASSIFICATION Crane with hook: CRANES I CLASSIFICATION Crane with hook: Usage class U5 Lift cylce Load lift Movement of the load Rotation Lowering Unhook the load Unloaded lift Rotation Movement of the load Unloaded lift To hook a new load tmc=150 s 22 CRANES I CLASSIFICATION Total length usage of the machine: T= N ⋅ t mc [h] 3600 tmc= cycle mean length [s] N = Number of cycles T= 5 ⋅105 ⋅150 ≈ 20835 horas 3600 CRANES I CLASSIFICATION For each of the mechanisms it is defined: αi = t mechanism t mc Load lift Movement of the load Rotation Lowering Unhook the load Unloaded lift Rotation Movement of the load Unloaded lowering Hook a new load tmechanism= usage time of the mechanism during one cycle [s] tmc= mean duration of one cycle [s] Lift mechanism Slewing mechanism Movement mechanism 23 CRANES I CLASSIFICATION Lift mechanism Load lift Movement of the load Rotation Lowering Unhook the load Unloaded lift Rotation Movement of the load Unloaded lowering Hook a new load Slew mechanism Load lift Movement of the load Rotation Lowering Unhook the load Unloaded lift Rotation Movement of the load Unloaded lowering Hook a new load 63% Travelling mechanism 25% Load lift Movement of the load Rotation Lowering Unhook the load Unloaded lift Rotation Movement of the load Unloaded lowering Hook a new load 10% CRANES I CLASSIFICATION Total duration of the mechanism in hours: αi=0.63 Lift mechanism Τi=13126 h Τ7 Slew mechanism αi=0.25 Τi=5209 h Travelling mechanism Τi=2084 h Τ5 αi=0.10 Τ4 24 CRANES I ENGINES • Power calculation: Lift movements G ⋅V Pe = 2 [CV] 4500 ⋅ η Travelling movements (G +G ) ⋅ W ⋅ V Pt = 1 2 [CV] 4500000 ⋅ η Power G1: self weight (trolley,span, etc.) [daN] G2: load + accessories [daN] V: speed [m/min] η: mechanical efficiency W: friction coefficient 7 for rolling bearing 20 for friction bearing CRANES I ENGINES Torque needed to accelerate: Starting torque = resistance torque + acceleration torque The resistance torque only has to be taken into account for travelling engines MA = Mw + Mb [daNm] Mw = 716 ⋅ Pt [daNm] n1 n1: engine speed in rpm ΣGD12: inertia torque sum referred to engine axis ta: acceleration time: Lift, cierre cuchara = 2 s Trolley travelling or bridge crane, rotation = 4 s Gantry travelling = 6 s d= V [m] π ⋅ n1 Mb = ∑ GD 2 1 ⋅ n1 375 ⋅ t a [daNm] Masses moved linearly GD12 = (G1 +G 2 ) ⋅ d 2 η [daNm 2 ] Rotating mass GD12 = GD 22 n 22 [daNm 2 ] n12 V: Mass lineal speed 25 CRANES I ENGINES CRANES I ENGINES Power needed to overcome wind resistance: Pv = S⋅ V ⋅ Fv [CV] 4500 ⋅ η Fv: wind pressure [daN/m2] S: surface exposed to wind To select travelling engine: Engine power ≥ Pt +Pv [CV] Max. motor toruque ≥ M w +M b [daNm] To select lift engine: Engine power ≥ Pe +Pv [CV] 26